U.S. patent application number 16/605584 was filed with the patent office on 2020-04-30 for method for determining process conditions to remove volatile organic compounds from polymer.
This patent application is currently assigned to LG Chem, Ltd.. The applicant listed for this patent is LG Chem, Ltd.. Invention is credited to Jae Hoon Choi, Je Seob Park, Won Chan Park.
Application Number | 20200129920 16/605584 |
Document ID | / |
Family ID | 64398393 |
Filed Date | 2020-04-30 |
![](/patent/app/20200129920/US20200129920A1-20200430-D00000.png)
![](/patent/app/20200129920/US20200129920A1-20200430-D00001.png)
![](/patent/app/20200129920/US20200129920A1-20200430-D00002.png)
![](/patent/app/20200129920/US20200129920A1-20200430-D00003.png)
![](/patent/app/20200129920/US20200129920A1-20200430-D00004.png)
![](/patent/app/20200129920/US20200129920A1-20200430-D00005.png)
![](/patent/app/20200129920/US20200129920A1-20200430-M00001.png)
![](/patent/app/20200129920/US20200129920A1-20200430-M00002.png)
![](/patent/app/20200129920/US20200129920A1-20200430-M00003.png)
![](/patent/app/20200129920/US20200129920A1-20200430-M00004.png)
![](/patent/app/20200129920/US20200129920A1-20200430-M00005.png)
View All Diagrams
United States Patent
Application |
20200129920 |
Kind Code |
A1 |
Park; Je Seob ; et
al. |
April 30, 2020 |
Method for Determining Process Conditions to Remove Volatile
Organic Compounds From Polymer
Abstract
The present application relates to a method for determining
process conditions to remove volatile organic compounds from a
polymer product through blowing. According to the method of the
present application, time and energy can be saved.
Inventors: |
Park; Je Seob; (Daejeon,
KR) ; Park; Won Chan; (Daejon, KR) ; Choi; Jae
Hoon; (Daejeon, KR) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
LG Chem, Ltd. |
Seoul |
|
KR |
|
|
Assignee: |
LG Chem, Ltd.
Seoul
KR
|
Family ID: |
64398393 |
Appl. No.: |
16/605584 |
Filed: |
April 23, 2018 |
PCT Filed: |
April 23, 2018 |
PCT NO: |
PCT/KR2018/004665 |
371 Date: |
October 16, 2019 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G16C 60/00 20190201;
G06F 30/20 20200101; G06F 2111/10 20200101; B01D 53/025 20130101;
B01D 53/30 20130101; G01N 2030/025 20130101; G01N 30/8675 20130101;
G01N 33/0047 20130101 |
International
Class: |
B01D 53/30 20060101
B01D053/30; G16C 60/00 20060101 G16C060/00; B01D 53/02 20060101
B01D053/02; G01N 33/00 20060101 G01N033/00; G01N 30/86 20060101
G01N030/86; G06F 30/20 20060101 G06F030/20 |
Foreign Application Data
Date |
Code |
Application Number |
Apr 24, 2017 |
KR |
10-2017-0052045 |
Apr 20, 2018 |
KR |
10-2018-0045985 |
Claims
1. A method for determining process conditions to remove volatile
organic compounds from a polymer by blowing a gas, comprising:
calculating a diffusion coefficient (D) and an equilibrium constant
(K) of the polymer; and simulating a process of removing the
volatile organic compounds based on the calculated diffusion
coefficient and equilibrium constant.
2. The method according to claim 1, wherein an amount of volatile
organic compounds is measured in a headspace of a container storing
the polymer, and the diffusion coefficient (D) and the equilibrium
constant (K) are calculated from the measured value.
3. The method according to claim 2, wherein the amount of volatile
organic compounds is measured in an equilibrium state of a system
defined by the sealed container containing the polymer.
4. The method according to claim 1, wherein the diffusion
coefficient (D) is calculated using the following relation equation
1 and the following formula: M 2 = B A M 1 [ Relation Equation 1 ]
M t M .infin. = 1 - 6 .pi. 2 n = 1 .infin. 1 n 2 exp ( - Dn 2 .pi.
2 t / a 2 ) [ Formula ] ##EQU00007## (wherein, in the Relation
Equation 1 above, A and B are amounts of volatile organic compounds
measured in headspaces of different containers, where A is an
amount of volatile organic compounds measured in the headspace of
the container containing the polymer not subjected to blowing and B
is an amount of volatile organic compounds measured in the
headspace of the container containing the polymer subjected to
blowing, and in the Formula above, t is a time for which the
blowing treatment is performed on the blown polymer to measure B, a
is a particle size of the polymer, D is the diffusion coefficient,
and the value of B/A is equal to the value of
M.sub.t/M.sub..infin..
5. The method according to claim 1, wherein the equilibrium
constant (K) is calculated using the following relation equation 2:
K = ( B A - B ) V g V s [ Relation Equation 2 ] ##EQU00008##
wherein, in the Relation Equation 2 above, A is an amount of
volatilized volatile organic compounds measured in the headspace
when one sealed container storing the polymer reaches a first
equilibrium state, B is an amount of volatilized volatile organic
compounds measured in the headspace, when the container is opened
for a predetermined time and sealed again after measuring the A and
then the container reaches a second equilibrium state, and V.sub.s
is a volume of the polymer stored in the container and V.sub.g is
the volume of the headspace.
6. The method according to claim 2, wherein the amount of volatile
organic compounds is measured using gas chromatography.
7. The method according to claim 1, wherein the diffusion
coefficient (D) and the equilibrium constant (K) are measured or
calculated at a plurality of temperatures, respectively.
8. The method according to claim 7, wherein it is assumed that the
simulating is a simulation of a process that a gas is blown into a
silo, in which a polymer is loaded and stored at a predetermined
height, for a predetermined time, the silo is equally divided into
n layers containing the polymer of the same loading height and the
gas flows from the first layer to the n-th layer sequentially.
9. The method according to claim 8, wherein for each of the
n-equally divided layers, energy balance and material balance are
calculated from the first layer to the n-th layer sequentially.
10. The method according to claim 9, wherein the simulating
comprises: inputting an initial value; firstly, using an energy
balance calculation between a polymer and a blowing gas present in
the n-th layer to calculate a changed temperature of the polymer
and a changed temperature of the blowing gas; secondly, calculating
an amount of volatile organic compounds discharged from the polymer
present in the n-th layer; and thirdly, calculating an amount of
the volatile organic compounds moving from the inside of the
polymer present in the n-th layer to the surface of the
polymer.
11. The method according to claim 10, wherein the initial value
comprises the equilibrium constant (K) and the diffusion
coefficient (D).
12. The method according to claim 11, wherein the initial value
further comprises one or more selected from the group consisting of
a size of a polymer, mass of a polymer, specific heat of a polymer,
density of a polymer, a temperature of a blowing gas, a flow rate
of a blowing gas, specific heat of a blowing gas, a blowing time of
a gas, a loading height of a polymer in a silo, a temperature of a
polymer, a number of layers in the divided silo, an amount of
volatile organic compounds contained in a polymer and a size of a
silo.
13. The method according to claim 10, wherein the calculating the
amount of volatile organic compounds discharged from the polymer
present in the n-th layer is calculated based on the equilibrium
constant (K) and the third step is calculated based on the
diffusion coefficient (D).
14. The method according to claim 10, wherein the amount of
volatile organic compounds that the polymer present in each layer
has on its surface or the change thereof is calculated as the
blowing time elapses.
15. The method according to claim 14, further comprising a step of
evaluating validity of an input initial value and determining
process conditions based on the calculated amount of the volatile
organic compounds or the change thereof.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of priority based on
Korean Patent Application No. 10-2017-0052045 filed on Apr. 24,
2017 and Korean Patent Application No. 10-2018-0045985 filed on
Apr. 20, 2018, the disclosures of which are incorporated herein by
reference in their entirety.
TECHNICAL FIELD
[0002] The present application relates to a method for determining
process conditions to remove volatile organic compounds from a
polymer.
BACKGROUND ART
[0003] Volatile organic compounds (VOC) are derived from the
residues of monomers, solvents, or other components used to make
polymer products. Volatile organic compounds remain inside the
product or on its surface even after manufacturing the product, and
slowly rise over the product surface or are released into the air
for a long period of time. These volatile organic compounds may
affect the hormone system of the human body through various routes
as well as they degrade quality and color senses of the product and
cause unpleasant odors.
[0004] A post-treatment, that is, removal of volatile organic
compounds from the produced polymer product, can be accomplished
through, for example, a method of exposing the product in a fresh
gas or a method of blowing a fresh gas into the product, and the
like. Preferably, it is necessary to remove as much volatile
organic compounds as possible and to this end, it should take a
long time to expose the product to the gas or blow the gas into the
product, but considering realistic factors such as a product
delivery time or production deadline, the time required for the
post-treatment cannot be indefinitely taken for a long time. In a
state where the properties are different for each polymer or each
volatile organic compound and the amount of volatile organic
compounds and its release rate are also unknown, it is not easy to
determine whether the removal process of volatile organic compounds
is performed under what conditions and for how much time.
DISCLOSURE
Technical Problem
[0005] It is one object of the present application to provide a
method for determining process conditions to remove volatile
organic compounds from a polymer.
[0006] It is another object of the present application to optimize
an amount of production, a production deadline and a delivery time
of a polymer product, and the like by selecting and regulating a
condition for exposing the polymer product to a gas.
[0007] The above objects and other objects of the present
application can be all resolved by the present application, which
is described in detail below.
Technical Solution
[0008] In one example of the present application, the method of the
present application is a method of determining process conditions
to remove volatile organic compounds from a polymer by blowing a
gas. The method comprises steps: calculating a diffusion
coefficient (D) and an equilibrium constant (K) of a polymer; and
simulating a removal process of volatile organic compounds based on
the calculated diffusion coefficient and equilibrium constant.
Advantageous Effects
[0009] According to the present application, there can be provided
a method of capable of analyzing a process of removing volatile
organic compounds present in a polymer product from the polymer
after simulation, and predicting and determining suitability of the
related process.
BRIEF DESCRIPTION OF DRAWINGS
[0010] FIG. 1 is shown to assist in understanding an experimental
method of calculating a diffusion coefficient (D) according to one
example of the present application.
[0011] FIG. 2 is shown to assist in understanding an experimental
method of calculating an equilibrium constant (K) according to one
example of the present application.
[0012] FIG. 3 shows a simulation order of a process, according to
one example of the present application.
[0013] FIG. 4 is a graph showing a result of simulating a process
of removing volatile organic compounds from a polymer based on
diffusion coefficients and equilibrium constants experimentally
obtained according to one example of the present application.
[0014] FIG. 5 is a graph showing process results in accordance with
change of diffusion coefficients and equilibrium constants
experimentally obtained according to one example of the present
application.
BEST MODE
[0015] The present application relates to a method for determining
process conditions to remove volatile organic compounds from a
polymer product by blowing a gas. The method may comprise steps of:
analyzing characteristics of a product; and simulating a process of
removing volatile organic compounds.
[0016] In the present application, the product or polymer product
may be referred to as a "polymer," and the characteristics of a
product may be "a diffusion coefficient" and "an equilibrium
constant." The diffusion coefficient and the equilibrium constant
can be analyzed experimentally. For example, the amount of volatile
organic compounds can be measured in a headspace of a container
storing a polymer to calculate the diffusion coefficient and
equilibrium constant from the measured values. The details are
described below.
[0017] In the present application, the terms "volatile organic
compound" and "polymer" are not limited to a specific compound or
polymer but may be used in a meaning embracing compounds that can
be referred to as volatile organic compounds in the related
technical field, and polymers that can be released from the
surface. The amount of volatile organic compounds (VOC) may be
referred to as total volatile organic compounds (TVOC).
[0018] In the present application, the "blowing" may mean a
treatment to cause or blow a flow of oxygen (O.sub.2) or nitrogen
(N.sub.2) or a gas containing it toward the polymer. The
temperature of the gas to be blown can be adjusted appropriately,
and the flow of a gas for blowing can be suitably caused by those
skilled in the art using known methods or equipment.
[0019] According to one example of the present application, the
method may comprise steps of: measuring an amount of volatile
organic compounds in a headspace of a container storing a polymer
to calculate a diffusion coefficient and an equilibrium constant
from the measured value; and simulating a removal process of the
volatile organic compounds based on the calculated diffusion
coefficient and equilibrium constant. The fact that is based on the
diffusion coefficient and the equilibrium constant means that the
diffusion coefficient and the equilibrium constant are used as an
initial value of the simulation, as described below.
[0020] Regarding the calculation of the diffusion coefficient and
the equilibrium constant based on the amount of the volatile
organic compounds measured in the headspace of the container, the
kind of the container storing the polymer is not particularly
limited. For example, a container including a body having a
predetermined volume and a cap capable of blocking physical
movement of a material between the inside and outside of the body,
such as a known vial, can be used. That is, it is sufficient that
the container usable in the present application can be opened and
closed, and if necessary, the inside of the container can be sealed
with an external environment. The measurement of the amount of
volatile organic compounds is performed on the premise that the
system defined by the sealed container containing the polymer is in
an equilibrium state.
[0021] The determination of the equilibrium state can be made by
measuring the change of the total volatile organic compounds plural
times over time. For example, if the amount of the volatile organic
compounds is measured several times from 30 minutes to 5 hours
while storing the polymer at a predetermined temperature such as
120.degree. C., the measured amounts of the volatile organic
compounds will converge to a constant value as the storing time
increases. That is, it can be determined that the equilibrium state
has been reached after the amount of the organic compounds has
become constant.
[0022] In the present application, the polymer may be stored in a
solid form in a container. For example, a polymer or a polymer
product can be stored in the form of powders or pellets (e.g.,
spheres or ellipses) in the container. At this time, the polymer
may be stored in the container in a volume smaller than the volume
of the container. The container can secure an internal space, that
is, a headspace, which is not occupied by the polymer product.
Accordingly, volatile organic compounds volatilized from the
polymer and a predetermined gas (e.g., air) can occupy the
headspace of the container.
[0023] In the present application, the method of measuring an
amount of the volatile organic compounds present in the headspace
of the container is not particularly limited. For example, the
amount of the volatile organic compounds present in the headspace
can be measured using gas chromatography. The unit representing the
amount of the volatile organic compounds is not particularly
limited.
[0024] With reference to the accompanying drawings, a method of
calculating the diffusion coefficient and the equilibrium constant
from the measured amount of the volatile organic compounds will be
described as follows.
[0025] FIG. 1 is shown to assist in understanding an experimental
method of calculating a diffusion coefficient (D) of volatile
organic compounds included in a polymer. In FIG. 1, two vials are
shown, in which pellet-shaped polymers prepared by the same method
from the same components are sealed and stored in the same amount,
respectively. However, the pellets stored in the right vial were
subjected to a blowing treatment and the pellets stored in the left
vial were subjected to no blowing treatment. The timing of the
blowing treatment for the pellets stored in the right vial is not
particularly limited. For example, after the polymer is stored in
the container, the blowing can be performed, or before the polymer
is stored in the container, the blowing can also be performed.
[0026] Specifically, in FIG. 1, M.sub.1 is the total amount of
volatile organic compounds that the polymer stored in the left vial
(Sample 1) has, M.sub.2 means the total amount of the volatile
organic compounds that the polymer stored in the right vial (Sample
2) has after being subjected to the blowing treatment. On the other
hand, when the amount of the volatile organic compounds volatilized
from the polymer stored in the left vial after storing the polymer
in the vial for a predetermined time, that is, the amount of the
gas-phase volatile organic compound present in the headspace of the
vial in Sample 1, is A, the amount of the remaining volatile
organic compounds that the solid polymer stored in the left vial
has (in the inside and/or on the surface) may be defined as
M.sub.1-A. Here, the predetermined time for which the polymer is
stored for measuring the content A may mean a time equal to or
longer than the minimum time that can be considered to have reached
the equilibrium state as described above. Similarly, when the
amount of the volatile organic compounds present in the headspace
of the right vial is B after storing the polymer in the right vial
for a predetermined period of time, the amount of the remaining
volatile organic compounds that the solid polymer of the right vial
have (in the inside and/or on the surface) may be defined as
M.sub.2-B.
[0027] In one example, the contents A and B can be measured on the
premise that the two samples have reached the equilibrium state at
the same temperature (t).
[0028] When they reach the equilibrium state at the same
temperature condition, the equilibrium constant (K) values obtained
from the respective vials shown in FIG. 1 are the same. Then, the
equilibrium constant (K) can be obtained through a ratio between
`the amount of volatile organic compounds that air in a unit volume
has in the headspace` and `the amount of volatile organic compounds
that the polymer in a unit volume has.` The polymer may have a
particle shape such as pellets. Accordingly, the following relation
equation 1 is established.
K = C s 1 C g 1 = C s 2 C g 2 [ Equation 1 ] - M 1 - A V s / A V g
= M 2 - B V s / B V g [ Equation 2 ] ##EQU00001##
[0029] Therefore, the following relation equation 1 is
obtained.
M 2 = B A M 1 [ Relation Equation 1 ] ##EQU00002##
[0030] In Equations above, C.sub.g1 is the amount of volatile
organic compounds that air in a unit volume has in the headspace in
Sample 1, and C.sub.s1 means the amount of volatile organic
compounds that the polymer in a unit volume has in Sample 1. In
addition, C.sub.g2 is the amount of volatile organic compounds that
air in a unit volume has in the headspace in Sample 2, and C.sub.s2
means the amount of volatile organic compounds that the polymer in
a unit volume has in Sample 2. Then, in each of Samples 1 and 2,
V.sub.s is the volume of the entire polymer in the vial, and
V.sub.g is the volume of the headspace, i.e., the volume of air
present in the headspace. In one example, V.sub.s can be obtained
from the density and weight of the selected pellets, and V.sub.g
can be obtained from the value of the internal volume of the used
container (vial) minus V.sub.s.
[0031] From Equations 1 and 2 and Relation Equation 1 concerning
the equilibrium constants as described above, it can be seen that
the ratio (B/A) value of the volatile organic compounds measured in
Samples 1 and 2, respectively is the same as M.sub.2/M.sub.1.
[0032] On the other hand, when volatile organic compounds are
released from spherical particles, the diffusion coefficient (D)
can be obtained by the following formula. Details of the formula
can be found in Chapter Diffusion in a sphere of The Mathematics of
Diffusion (2nd Edition), which is J. Crank's book.
M t M .infin. = 1 - 6 .pi. 2 n = 1 .infin. 1 n 2 exp ( - Dn 2 .pi.
2 t / a 2 ) [ Formula ] ##EQU00003##
[0033] The formula is that the formula in the integral form
associated with the calculation of the diffusion coefficient is
changed to the form of infinite series. Therefore, it may be
correct to use the formula after summing up the calculated values
from the case where the value of n is 1 to the case where it is
infinite, but since there is n.sup.2 in the denominator, when n is
an integer exceeding about 10, the effect of the n value is not
significant. In other words, in the formula, it is also fine to
perform the calculation only when n is from 1 to 10.
[0034] In the formula, M.sub..infin. is the total amount of
volatile organic compounds that the particles can discharge for the
infinite time (i.e., while reaching the equilibrium sate without
blowing), and M.sub.t is the total amount of volatile organic
compounds that the particles have after the particles discharge the
volatile organic compounds for a certain time through blowing.
Thus, M.sub..infin. may correspond to M.sub.1 as described above,
and M.sub.t may correspond to M.sub.2 as described above. As a
result, it can be said that the value of B/A measured in the
headspace is equal to the value of M.sub.t/M.sub..infin.. And, in
the formula, t may be the blowing time (an example of unit: hour),
and a may be the particle size of the polymer (an example of unit:
mm). Consequently, when these values are substituted into the
formula, the D value described in the formula, that is, the
diffusion coefficient can be obtained.
[0035] FIG. 2 is shown to assist in understanding the calculation
of the equilibrium constant (K) of the volatile organic compounds
contained in the polymer. As shown in FIG. 2, after one sample
sequentially reaches two equilibrium states, the equilibrium
constant (K) can be obtained through the amount of volatile organic
compounds in the headspace measured in each equilibrium state.
[0036] Specifically, as shown in FIG. 2, a polymer containing
volatile organic compounds as much as M.sub.0 (for example, a
polymer having a particle shape such as pellets) is sealed and
stored in one container (e.g., vial), and stored for a
predetermined time so as to be capable of reaching a first
equilibrium state. When the amount of the volatile organic
compounds present in the headspace after a lapse of a predetermined
time is A, the amount of the volatile organic compounds remaining
in the polymer may be defined as M.sub.0-A. Then, the inner gas of
the sample is replaced through a method of opening the cap of the
vial, or the like, and the cap is closed again. The opening time is
not particularly limited. After a lapse of a predetermined time, it
reaches a second equilibrium state, and then when the amount of the
volatile organic compounds present in the headspace is B, the
amount of volatile organic compounds remaining in the polymer may
be defined as M.sub.0-A-B. At this time, the first and second
equilibrium states may be formed at the same temperature (t').
[0037] When the equilibrium states are reached at the same
temperature condition, the values of the equilibrium constant (K)
obtained in the first and second equilibrium states shown in FIG. 2
are the same. Then, the equilibrium constant (K) can be obtained
through a ratio between `the amount of volatile organic compounds
that air in a unit volume has in the headspace` and `the amount of
volatile organic compounds that the polymer in a unit volume has.`
In the following equations 3 and 4, however, V.sub.s is the volume
of the entire polymer in the vial and V.sub.g is the volume of the
headspace, i.e., the volume of air present in the headspace, where
these values are values already known at the time of vial selection
and introduction of the polymer.
K = M 1 - A V s / A V g = M 2 - A - B V s / B V g [ Equation 3 ] -
M 0 = A 2 A - B [ Equation 4 ] ##EQU00004##
[0038] If the result of Equation 4 above is substituted into
Equation 3, the following relation equation 2 can be obtained.
K = ( B A - B ) V g V s [ Relation Equation 2 ] ##EQU00005##
[0039] Consequently, A and B can be measured through gas
chromatography, and since the values of V.sub.s and V.sub.g are
already known values, the equilibrium constant (K) can be obtained
through Relation Equation 2 above.
[0040] In one example, the equilibrium state temperatures used to
obtain the equilibrium constant (K) and the diffusion coefficient
(D), respectively, may be the same or different. For example, both
the equilibrium constant and the diffusion coefficient can be
calculated at 60.degree. C. Alternatively, the equilibrium constant
and the diffusion coefficient may be analyzed at 40.degree. C.,
60.degree. C. and 80.degree. C., and then the diffusion coefficient
and the equilibrium constant at 50.degree. C. may be deduced and
used in the method of the present application. For example, K
values obtained at three temperatures (T) of 40.degree. C.,
60.degree. C. and 80.degree. C. are used to be substituted into
K=10.sup.((b/T)-C), whereby b and C can be obtained and then the K
value at a specific temperature T can be obtained. The used formula
can be found in B. Kolb & L. Ettre' book, `Static Headspace-Gas
Chromatography.`
[0041] In another example, the values of the equilibrium constants
and/or the diffusion coefficients may be calculated at a plurality
of temperatures. For example, the values of the equilibrium
constant and the diffusion coefficient at each temperature can be
calculated at 0.1.degree. C. intervals, 0.5.degree. C. intervals,
1.degree. C. intervals, 2.degree. C. intervals or 3.degree. C.
intervals in a temperature range of 20.degree. C. to 100.degree. C.
The values calculated at a plurality of temperatures can be
appropriately used at a stage where the corresponding value is
required in a simulation process to be described below.
[0042] According to the method of the present application, it is
possible to simulate a process of removing volatile organic
compounds from a polymer based on the diffusion coefficient and the
equilibrium constant calculated in the above manner. Assuming that
the polymer is subjected to blowing in a state where the diffusion
coefficient and the equilibrium constant, and the like are known,
the simulation is that the results are confirmed. After confirming
the results, suitability of process conditions, and the like can be
interpreted. For example, in the case of simulating a blowing
process performed under a predetermined condition, it is possible
to check how the TVOC changes with time as in FIG. 4, where the
suitability of process conditions is interpreted through the
confirmed results.
[0043] Specifically, the blowing process to be simulated is assumed
to be a process of blowing a gas having a predetermined temperature
into a silo loading and storing the polymer at a predetermined
height. Then, the simulation is performed while energy balance,
material balance and/or their changes in the silo are calculated.
In one example of this simulation process, the polymer loaded and
stored in the silo may be in the form of particles, such as, for
example, pellets. In another example of the simulation process, the
gas to be blown has a temperature higher than the polymer, which
may be referred to as hot air. Furthermore, the silo may have a
cylinder or column shape, and may be assumed to be unaffected other
than the matters considered in the present application.
[0044] A predetermined program may be used for this simulation. For
example, the calculation involved in each step of the simulation
may be performed by instructions being executable by a processor
and stored on a computer-readable medium. Then, the results of the
simulation can be viewed by a performer of the method according to
the present application through a display device interlocked with
the program performing each step.
[0045] In one example, the silo and the polymer can be assumed to
be divided into n in the loading height direction. For example, in
the case where the loading height of the polymer in the silo is 10
m, it can be assumed that if the loaded polymer is evenly divided
into 100, one unit of the polymer loaded at a height of 10 cm is
present in each of layers equally divided into 100 (may be referred
to as unit or unit cell). That is, it can be assumed that the silo
is equally divided into n layers including a polymer having the
same loading height. Then, it can be assumed that each of the
divided silos secures an extra space (e.g., headspace) in which the
volatile organic compounds released from the polymer can exist.
Then, the energy balance and the material balance can be
sequentially calculated for each of the layers. For example, the
energy balance and the material balance can be sequentially
calculated from the first layer to the n-th layer by a method that
the energy balance and the mass balance are calculated while the
blown gas passes through the first layer and the same calculation
is performed even if the gas passing through the first layer
continuously passes through the second layer. At this time, the
energy balance and the material balance calculated in association
with the n-1-th layer can be used for the energy balance and the
material balance calculation of the n-th layer.
[0046] A specific simulation process will be described with
reference to FIG. 3.
[0047] As in FIG. 3, the simulation may comprise a step of
inputting an initial value including a diffusion coefficient and an
equilibrium constant. That is, the simulation of the blowing
process is performed based on predetermined information related to
process conditions. Specifically, in order to simulate the blowing
process, some information related to the process may be inputted as
an initial value into the program used to perform the method of the
present application. As the initial value, the experimentally
calculated diffusion coefficient and equilibrium constant can be
used.
[0048] In one example, other information besides the diffusion
coefficient and equilibrium constant may be used together as an
initial value. For example, one or more selected from the group
consisting of a size of a polymer (e.g.: diameter of a particle
type polymer), characteristics of a polymer (e.g.: mass, specific
heat and/or density), a temperature of a blowing gas, a flow rate
of a blowing gas, specific heat of a blowing gas, a blowing time of
a gas, a loading height of a polymer in a silo, bulk density of a
polymer loaded in a silo, a temperature of a polymer, the number of
layers in the divided silo, TVOC contained in a polymer, and a size
of a silo (e.g.: diameter) may be used as additional initial
values.
[0049] In FIG. 3, the time step means a time during which in the
case where the polymer is divided into n layers, interpretation
(calculation of material balance and energy balance) from the first
to the n-th layers is performed only once without repetition. For
example, assuming that the number of repetitions of interpretation
from the first to the n-th layers is 100 and the total
interpretation time is 100 seconds, the time step means 1 second.
In other words, if the interpretation according to the one time
step performed for one second is repeated 100 times, the time
required for the total time steps, that is, the total
interpretation time is 100 seconds. In the present application, the
interpretation as above is made during the time that the gas is
blown. In other words, the total time for which the interpretation
as above is performed means the total time for which the blowing is
performed, and the time step, which is a time for which the
above-described one time analysis is performed, is a concept
defined for the simulation, which can mean the unit time when a
fresh gas (divided from the first layer to n-th layer) is blown
into a silo. Consequently, in the present application, the total
interpretation time, i.e., the total blowing time, can be divided
into a plurality of time steps. In some cases, the gas may be seen
to flow continuously or discontinuously into the silo during one
unit of time step.
[0050] Furthermore, in the present application, it can be assumed
that a fresh gas is periodically blown into the first layer of the
silo when the order of the time steps is changed. For example, if
the analysis during the first time step performed assuming that the
fresh gas continuously passes through from the first layer to the
n-th layer is completed, the second analysis, that is, the second
time step, in which the fresh gas again passes through from the
first layer to the n-th layer, begins.
[0051] With respect to the analysis, the n-th calculated value can
affect the calculated value of the n+1-th layer, and the calculated
value at the m-th time step can affect the calculated value at the
m+1-th time step. It will be explained in more detail in the
related contents.
[0052] Considering accuracy of the interpretation, the shorter the
physical time of one time step, the better. Even if the total time
required for the interpretation is the same, the shorter the
physical time of one time step, the number of interpretation from
the first to the n-th layers can increase and the accuracy can
increase. For example, it is preferred that one time step is set to
mean a time of several seconds to tens of seconds. Also, the
interval between time steps is also preferably as short as
possible.
[0053] Specifically, the simulation may comprise: a first step of
using an energy balance calculation between a polymer and a blowing
gas present in the n-th layer to calculate a changed temperature of
the polymer and a changed temperature of the blowing gas; a second
step of calculating an amount of volatile organic compounds
discharged from the polymer present in the n-th layer; and a third
step of calculating an amount of the volatile organic compounds
moving from the inside of the polymer present in the n-th layer to
the surface of the polymer.
[0054] In one example, the first step may be a step of using an
energy balance calculation between the polymer and the blowing gas
of the n-th layer to calculate `the elevated temperature of the
polymer increased by the gas blown at the n-th layer` and `the
temperature of the gas (hot air) decreased after blowing at the
n-th layer.`
[0055] Specifically, in order to allow the volatile organic
compounds on the surface of the polymer to be discharged into the
air, the gas to be blown may have a temperature higher than the
temperature of the polymer or the temperature of the air occupying
an empty space in the silo assuming that the polymer is stored (for
convenience of explanation only, the temperature of the gas flowing
into the unit layer is not always higher than the temperature of
the polymer present in the relevant layer). When the
high-temperature gas or the hot air is blown as above, the thermal
energy of the high-temperature gas is transferred to the polymer,
and thus the temperature of the polymer consequently increases as
compared with that before blowing, and the temperature of the blown
gas decreases. The energy balance between the polymer (particle)
and the gas to be blown can be expressed as Equation 5 below.
Q=H.times.A.times.(T.sub.A-T.sub.s) [Equation 5]
[0056] In Equation 5 above, Q is the energy supplied to the polymer
by the gas to be blown, which may have a unit such as W or J. Then,
H is a convection heat transfer coefficient, A is an area of
particles, T.sub.A is a temperature of the blowing gas, and T.sub.s
is a surface temperature of the polymer. The thermal conductivity H
of a polymer can be known from known material information or a
known relationship, and Ts or T.sub.A is one of the initial input
values as described above.
[0057] When the thermal energy Q transmitted to the polymer
(particle) by the hot air is obtained through Equation 5 above,
`the temperature of the polymer raised by the hot air` and `the
temperature of the hot air dropped after the thermal energy is
transmitted to the polymer` can be calculated, respectively. For
example, when the Q value is divided by the mass and the specific
heat value of the polymer, respectively, the temperature change
amount (.DELTA.T) of the polymer can be known, and when the
temperature change amount is added to the Ts value, the final
temperature of the polymer increased by hot air can be known.
Similarly, when the Q value is divided by the mass and the specific
heat value of the air, respectively, the temperature change amount
(.DELTA.T') of the air can be known, and when the temperature
change amount is added to the T.sub.A value, the final temperature
of the air decreased while being blown can be known.
[0058] The `temperature of the blowing gas dropped in the n-th
layer` thus obtained can be used as the temperature of the gas
flowing (blowing) into the n+1-th layer at the same time step.
Then, `the elevated temperature of the polymer in the n-th layer`
thus obtained can be used as the temperature of the polymer present
in the n-th layer in the next time step.
[0059] In one example, the second step may be a step of calculating
an amount (X) of volatile organic compounds discharged from the
polymer in the n-th layer. At this time, the equilibrium constant
(K) calculated through experimental measurement may be used.
[0060] The amount (X) of volatile organic compounds can be regarded
as an amount of the compounds present on the surface of the
polymer, which are the volatile organic compounds volatilized from
the polymer through blowing. In other words, the amount (X) of the
discharged volatile organic compounds is the amount of the volatile
organic compounds contained in the blowing gas introduced into the
n-th layer. That is, it is the amount of volatile organic compounds
in the hot air present in the n-th layer.
[0061] To calculate the amount (X) of the volatile organic
compounds in the hot air, the previously calculated equilibrium
constant (K) may be used. That is, when the hot air is blown, the
amount of the volatile organic compounds volatilized from the
surface of the polymer to be included in the hot air is determined
by the equilibrium constant. The equilibrium constant (K) may be
expressed as a ratio of `the amount (VOCs) of the volatile organic
compounds present on the surface of the polymer (particle) in the
unit volume` to `the amount (X) of the volatile organic compounds
in the unit volume of air.` That is, an equilibrium constant
(K)=(VOCs/V.sub.s)/(X/V.sub.A). Consequently, the amount (X) of the
volatile organic compounds can be obtained as in Equation 6
below.
Amount (X) of volatile organic
compounds={(VOCs/V.sub.s)/(K)}.times.V.sub.A) [Equation 6]
[0062] In Equation 6 above, VOCs is an amount of volatile organic
compounds present on the surface of the polymer, V.sub.s is a
volume of the polymer surface layer, V.sub.A is a volume of the gas
to be blown, and K is an equilibrium constant.
[0063] With regard to Equation 6 above, it can be assumed that the
polymer is formed by layering a plurality of spheres having
different diameters, where V.sub.s means a (inner) volume that the
surface of the outermost sphere has. In some cases, it is necessary
to check the number of particles when calculating the VOCs. The
number of particles can be known from the already known diameter of
the silo, the particle loading height, and the bulk density at
which the particles are loaded.
[0064] With regard to Equation 6 above, the VOCs may be a value
measured for a sample that has not been subjected to blowing in the
calculation procedure of the experimental diffusion coefficient (D)
as described above. Then, K is the initial value known from the
experimental calculation, V.sub.A is one of the initial values as
the flow rate of the hot air, that is, the gas to be blown, and
V.sub.s is the size of the polymer, which is a value that can be
known as one of the initial values. In one example, the K value may
be one or more of the K values at various temperatures as
previously obtained experimentally, where the temperature may be a
temperature of the gas blown to the layer.
[0065] As described above, as the volatile organic compounds have
moved from the surface of the polymer to the air, the amount of the
volatile organic compounds contained in the gas blown to the n+1-th
layer increases, and on the basis of this, the discharge amount of
the volatile organic compounds at the n+1-th layer is calculated.
Specifically, the amount (X) of the volatile organic compounds
contained in the gas blown in the n-th hot air can be used as the
amount of the volatile organic compounds contained in the gas
flowing into the n+1-th layer. In one example, when a gas having
volatile organic compounds in an amount of X is blown to the n+1-th
layer, it can be confirmed using an equilibrium constant (K)
whether the volatile organic compounds are further discharged (or
volatilized) from the polymer having a predetermined amount of
volatile organic compounds on the surface (present at the n+1-th).
Specifically, when the value of the equilibrium constant K.sub.N+1
obtained through `the amount of volatile organic compounds that the
polymer in a unit volume contained in the n+1-th layer has` and
`the amount (X) of volatile organic compounds that the gas in a
unit volume blown into the n+1-th layer has` is smaller than the
value of the experimentally obtained equilibrium constant K, it can
be seen that the additional discharge of the polymer can also occur
at the n+1-th layer.
[0066] In one example, it can be assumed that the amount (X) of
volatile organic compounds has little effect on the next ranked
time step.
[0067] In one example, the third step may be a step of calculating
an amount (Y) of volatile organic compounds moving from the inside
of the polymer present in the n-th layer to the surface of the
polymer. As previously described, when the volatile organic
compounds are volatilized from the surface of the polymer to air, a
concentration gradient of the volatile organic compounds occurs
between the inside and the surface of the polymer, and thus the
volatile organic compounds inside the polymer move to the surface
of the polymer. Then, the amount of volatile organic compounds
moving from the inside of the polymer to the surface of the polymer
can be calculated based on the diffusion coefficient (D). For
example, the amount (Y) of the volatile organic compounds moving
from the inside of the polymer to the surface of the polymer can be
calculated by Equation 7 below, which is a diffusion control
equation in a spherical polymer (particle).
.differential. C .differential. t = 1 r 2 .differential.
.differential. r { r 2 D .differential. C .differential. r } [
Equation 7 ] ##EQU00006##
[0068] In Equation 7 above, t is a time, D is a diffusion
coefficient, r is a radius of the polymer (particle), and C is a
concentration. In one example, the D value may be one or more of
the D values at various temperatures as previously obtained
experimentally, where the temperature may be a temperature of the
gas blown to the relevant layer. The amount (Y) of volatile organic
compounds on the surface of the polymer moving from the inside of
the polymer to the surface of the polymer during the blowing time
can be obtained by calculating the change in the concentration with
time.
[0069] The amount (Y) of volatile organic compounds thus obtained
on the surface of the polymer can be used as the amount (VOCs) of
volatile organic compounds on the surface of the polymer used in
association with Equation 6 at the next time step.
[0070] In one example, it can be assumed that the amount (Y) of
volatile organic compounds on the surface of the polymer has little
effect on the n+1-th layer.
[0071] Consequently, in the case of performing the first to third
steps as above, that is, as a result of the simulation, (a) the
temperature of the polymer, (b) the amount (TVOC) of volatile
organic compounds present in the inside and/or on the surface of
the polymer, (c) the temperature of the gas blown or to be blown,
and (d) the amount (TVOC) of volatile organic compounds contained
in the gas blown or to be blown can be known. Among these, (b) the
amount (TVOC) of volatile organic compounds present in the inside
and/or on the surface of the polymer can be directly used
(calculated) for the analysis of the simulation results.
[0072] In one example, the simulation results can be analyzed
through an average (Y.sub.avg) of the amount of volatile organic
compounds on the surface of the polymer present in each layer after
the total interpretation time is over. For example, by obtaining an
arithmetic average value (Y.sub.avg) for the amount of volatile
organic compounds measured in the layer for each time step and
confirming the decreasing trend of the value (Y.sub.avg) over time,
that is, according to the increase of the time step, the reduction
degree of the volatile organic compounds according to the blowing
conditions can be compared (see FIG. 4).
[0073] In one example, the method may further comprise a step of
evaluating suitability or validity of process conditions based on
the simulation results and reflecting it in the process conditions.
For example, if the result according to the input initial value is
appropriate as the current situation, the conditions input as the
initial value can be determined as conditions of the actual blowing
process, and otherwise, other conditions can be input to perform
the simulation again.
[0074] With reference to FIGS. 4 and 5, the process of performing
the method of the present application will be described in detail
as follows.
[0075] FIG. 4 shows a result of simulating a process of removing
volatile organic compounds from a polymer based on empirically
obtained diffusion coefficients and equilibrium constants, as
described above. The process of obtaining diffusion coefficients
and equilibrium constants on which the simulation is based, and the
analysis of the simulation results are as follows.
[0076] Calculation of Equilibrium Constants
[0077] As previously described with reference to FIG. 2, for one
vial sample storing a pellet-shaped polymer in a predetermined
volume, the gas inside the vial was changed once between first and
second equilibrium states so that two equilibrium states could be
obtained sequentially. The amount of volatile organic compounds in
the headspace measured at each equilibrium state was measured by
gas chromatography at 60.degree. C. Since the weight of the used
pellets was 2 g and the density of the polymer constituting the
pellets was 1,070 kg/m.sup.3, the volume V.sub.s (about 1.87 ml) of
the pellets could be obtained from them. On the other hand, as the
volume of the headspace, that is, the volume V.sub.g of gas (air),
the value obtained by subtracting V.sub.s (about 1.87 ml) from the
volume 20 ml of the used vial was used.
[0078] In this regard, the TVOC values measured in the first and
second equilibrium states and the equilibrium constant (K) obtained
according to Relation Equation 2 are as shown in Table 1 below. The
known VDA277 method was used upon measuring the amount (TVOC) of
volatile organic compounds.
TABLE-US-00001 TABLE 1 TVOC (ppm) Equilibrium Constant (K) First
equilibrium 157.2 124.1 state (at 60.degree. C.) Second equilibrium
145.8 state (at 60.degree. C.)
[0079] Calculation of Diffusion Coefficients
[0080] As previously described with reference to FIG. 1, two groups
of pellet-shaped polymers (particle size: 3 mm), which differed
only in the presence or absence of the blowing treatment, were
stored in two vials different from each other, respectively, and
the amount of volatile organic compounds in the headspace measured
at each equilibrium state was measured by gas chromatography at
60.degree. C. The blowing treatment associated with Sample 2 was
done for 2 hours. The size of the vial and the volume and weight of
the polymer are the same as described above.
[0081] Using the above-described formula, D was obtained.
Specifically, the M.sub.t/m.sub..infin. value of the formula was
replaced by the B/A value, the particle size (3 mm) was substituted
for a, and 2 hours was substituted for t relating to the blowing
time. For reference, upon applying the formula above, the values
from the case where n is 1 to the case where n is 10 were added
up.
[0082] In this regard, the TVOC values measured in the equilibrium
states of Sample 1 and Sample 2 and the value of the diffusion
coefficient (D) obtained according to the formula are as shown in
Table 2 below.
TABLE-US-00002 TABLE 2 TVOC of Sample 1 TVOC of Sample 2 Diffusion
(ppm) (Reference) (ppm) (after blowing) Coefficient (D) Temper-
273.5 ppm 43.2 ppm 4.33 .times. 10.sup.-11 ature (60.degree.
C.)
[0083] Simulation of Process
[0084] The process was simulated based on the calculated diffusion
coefficient (D) and equilibrium constant (K). The initial values
input in relation to the simulation are as shown in Table 3.
[0085] [Initial Value Information] [0086] Diffusion coefficient
(D): 4.33.times.10.sup.-11 at 60.degree. C.
[0087] (However, upon changing the temperature, it is calculated by
4.19.times.10.sup.-12.times.exp(-0.03814T), where T is a
temperature) [0088] Equilibrium constant: 124.1 at 60.degree.
C.
[0089] (However, upon changing the temperature, it is calculated by
K=10.sup.(1181.85/T-1.51187), where T is a temperature) [0090]
Polymer (particle) relation: diameter 3 mm, mass 2 g, specific heat
1500 J/kgK, density 1,070 kg/m.sup.3, thermal conductivity 0.22
W/mK [0091] Blowing gas: temperature 70.degree. C., flow rate 1,000
kg/hr, specific heat 1000 J/kgK, convection heat transfer
coefficient 2 W/m.sup.2K [0092] Blowing time: 1200 minutes [0093]
Loading height of polymer in silo: 4.5 m [0094] Silo: height 4.5 m,
diameter 1.5 m, bulk density 500 kg/m.sup.3 [0095] Polymer
temperature: 50.degree. C. [0096] Number of layers in divided silo:
1,000 [0097] TVOC contained in polymer: 275.3 ppm
[0098] Specifically, the simulation related to FIG. 4 records how
the amount of volatile organic compounds changes in a plurality of
silos as the blowing time for the polymer particles (pellets)
loaded in the silo increases, where the results of the case in
which the pellet temperature is changed (Case 1) and the case in
which the flow rate of the hot air is changed (Case 2) are compared
and shown on the basis of a reference controlled to have
predetermined pellet temperature and blowing (hot air) flow rate.
In the graph of FIG. 4(a), the Y-axis values are calculated as the
reduced ratios according to the blowing time, relative to the
amount of the initial volatile organic compounds, and the X-axis
means the blowing time. Based on the dotted line drawn at a height
of a value of about 0.1 in the Y-axis, it can be seen that if it is
difficult to change the temperature of the pellet particles or the
blowing flow rate, at least a blowing time of at least 240 minutes
should be secured. On the contrary, it can be seen that if the
change of the blowing time, that is, the silo residence time is
impossible, the temperature of the pellet particles should be
raised or the flow rate of hot air should be increased.
Consequently, the method of the present application can be used to
determine process conditions such as the blowing time, the blowing
flow rate, or the temperature of the pellets required to obtain the
desired (residual) amount of volatile organic compounds. FIG. 4(b)
is the results of analysis through the absolute amount of TVOC.
[0099] FIG. 5 also shows a result of simulating a process of
removing volatile organic compounds from a polymer based on
empirically obtained diffusion coefficients and equilibrium
constants, as described above. In FIG. 5, the diffusion coefficient
value and the equilibrium constant value of the reference are the
same as those of the reference used in the simulation of FIG. 4.
Specifically, in the simulation of FIG. 5(a), the results of the
case where the diffusion coefficient was increased twice (Case 3)
and the case where the equilibrium constant was increased twice
(Case 4) were compared (other blowing conditions were the same). It
can be seen through Case 3 that when the diffusion coefficient is
increased, the decreasing amount of volatile organic compounds is
larger even if the blowing time is the same. In addition, it can be
seen through Case 4 that when the equilibrium constant is
increased, the equilibrium state is easily reached even if a small
amount of volatile organic compounds is discharged into the air,
and as a result, the volatile organic compounds are no longer
discharged from the particles. These results are in agreement with
the meaning of the diffusion coefficient related to the diffusion
rate of the volatile organic compounds discharged from the inside
of the particles and the meaning of the equilibrium constant
concerning the ratio of the amount of the volatile organic
compounds possessed by the particles per unit volume to the amount
of the volatile organic compounds possessed by the blowing gas per
unit volume. In addition, this may mean that the diffusion
coefficient and equilibrium constant may be important factors in
the removal of volatile organic compounds through blowing. FIG.
5(b) shows the results through the absolute amount.
* * * * *